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General Optics Design Part 2

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General Optics Design Part 2 GENERAL OPTICS DESIGN PART 2 Martin Traub – Fraunhofer ILT [email protected] – Tel: +49 241 8906-342 © Fraunhofer ILT AGENDA Raytracing Fundamentals Aberration plots Merit function Correction of optical systems Optical materials Bulk materials Coatings Optimization of a simple optical system, evaluation of the system Seite 2 © Fraunhofer ILT Why raytracing? • Real paths of rays in optical systems differ more or less to paraxial paths of rays • These differences can be described by Seidel aberrations up to the 3rd order • The calculation of the Seidel aberrations does not provide any information of the higher order aberrations • Solution: numerical tracing of a large number of rays through the optical system • High accuracy for the description of the optical system • Fast calculation of the properties of the optical system • Automatic, numerical optimization of the system Seite 3 © Fraunhofer ILT Principle of raytracing 1. The system is described by a number of surfaces arranged between the object and image plane (shape of the surfaces and index of refraction) 2. Definition of the aperture(s) and the ray bundle(s) launched from the object (field of view) 3. Calculation of the paths of all rays through the whole optical system (from object to image plane) 4. Calculation and analysis of diagrams suited to describe the properties of the optical system 5. Optimizing of the optical system and redesign if necessary (optics design is a highly iterative process) Seite 4 © Fraunhofer ILT Sequential vs. non sequential raytracing 1. In sequential raytracing, the order of surfaces is predefined very fast and efficient calculations, but mainly limited to imaging optics, usually 100..1000 rays 2. In non-sequential raytracing, each ray may hit (or miss) each surface as often as necessary, and rays can be absorbed, new rays are generated at partially reflecting surfaces… limited possibilities for optimization, usually > 106 rays Non-sequential: Sequential: Camera lens laser pump cavity Seite 5 © Fraunhofer ILT Description of an optical system Sf2 Sf3 Sf0 Sf1 Sf3 r (Ob- 1 (Image) ject) th0 th1 th2 th3 sd1 n2 (n0,1,3=1) sd3 r2 The optical system is defined by a sequence of surfaces (Sf0 to Sfn). Each surface is defined by 1) Curvature 2) Distance to the next surface 3) Semi diameter 4) Index of refraction of the material following the surface Seite 6 © Fraunhofer ILT Example of traced rays Image Chief ray plane Marginal ray Object plane • A number of rays is traced through the optical system • Between two surfaces, the rays are straightly propagating • At each interface with a change in index, refraction or reflection occurs • The beam deflection is calculated applying the full law of refraction (the example shows the marginal and the chief ray) Seite 7 © Fraunhofer ILT Definition of the field of view by the object size • Image of an 28 object formed 35 by a three-lens system (not 24 well corrected) B( =8) • Object size: 24 mm • The ray bundle of each object point is limited by the aperture B • To describe the system, ray bundles for different object points are calculated (here: +/-12, +/- 6, and 0 mm) • As the system is symmetrical, rays below the optical axis are usually neglected Seite 8 © Fraunhofer ILT Definition of the field of view by field angle = 0, 6, 12° 20 B ( = 14) • If objects located far from the optical systems are imaged, the incoming rays are nearly parallel (e.g. stars) • Therefore, the field of view is defined by the angle formed by the chief rays and the optical axis Seite 9 © Fraunhofer ILT Abberation plots Raytracing software offer a number of diagrams and plots for analyzing the aberrations of an optical system: • Wave front aberrations (Optical Path Difference: OPD) TRF • Transverse ray aberration (Transverse Ray Fan: TRF) • Spot diagrams • Encircled energy plots • Modulation transfer function (MTF) • Point Spread Function (PSF) encircled energy OPD Spot Seite 10 © Fraunhofer ILT Normalized coordinates Raytracing software uses normalized cartesian coordinates rather than polar coordinates (r, ) to define the position of a ray in the entrance pupil. y sin x Px RP RP cos y Py RP RP R P x RP – pupil radius © Fraunhofer ILT Ray definition Raytracing software uses two points to define each ray: one is located in the object plane, and the other is located in the entrance pupil. Entrance Pupil Tangential Plane Sagittal Plane Object Plane © Fraunhofer ILT Calculation of the OPD • Calculation of the optical path length q (x,y) for a number (i,j) of rays located in the entrance pupil: li,j Reference Sphere • Normalized to the wavelength and Δy composed to a R wavefront field Optical System Image plane W(x,y) (Detector plane) • Calculation of the spherical reference wave Wsph,Ref • The OPD q(x,y) (wave front aberration) is calculated by q(x,y) = W(x,y) - Wsph,Ref(x,y) • The transverse ray aberrations can be calculated by: R q R q x y n n Seite 13 x y © Fraunhofer ILT Example: OPD for a system with spherical aberrations • Uncorrected singled with large spherical aberrations • The complete 2D OPD (wavefront map) as a function of Px and Py is shown on the right hand side Px Py • Usually only x and y cross sections are given (OPD fan) Seite 14 © Fraunhofer ILT Abberation plots Raytracing software offer a number of diagrams and plots for analysing the aberrations of an optical system: • Wave front aberrations (Optical Path Difference: OPD) TRF • Transverse ray aberration (Transverse Ray Fan: TRF) • Spot diagrams • Encircled energy plots • Modulation transfer function (MTF) • Point Spread Function (PSF) encircled energy OPD Spot Seite 17 © Fraunhofer ILT Transverse Ray Fan (TRF) Plot a b Detector Py ∆y/ 3 plane C040 · y Py ∆y(b) ∆y(a) Px,y - Normalized pupil coordinates ∆x, ∆y - Transverse distance from the axis or the chief ray if the ray bundle is tilted to the optical axis The aberration is measured in wavelengths Seite 18 © Fraunhofer ILT Abberation plots Raytracing software offer a number of diagrams and plots for analysing the aberrations of an optical system: • Wave front aberrations (Optical Path Difference: OPD) TRF • Transverse ray aberration (Transverse Ray Fan: TRF) • Spot diagrams • Encircled energy plots • Modulation transfer function (MTF) • Point Spread Function (PSF) encircled energy OPD Spot Seite 19 © Fraunhofer ILT Spot diagram Spot diagram Field angle = 10° • Start: field of rays Image plane in the entrance pupil with a specific pattern • Calculation and plot of all Field angle = 0° intersection points of rays on the image plane V:\A991\2004\VORTRAG\VORLESUNG_TOS_I\05_RayTracing\Links\ZemaxBeis piele\SpotDiagram.ZMX • Gives a good overview of the Intersection points aberrations of the of the rays on the = 0° optical system image plane Seite 20 © Fraunhofer ILT Spot diagram: Start patterns Hexapolar distribution Hexapolar: (rotationally symmetric) • Artifacts • Well suited for 3rd Square distribution order aberrations Square: • Artifacts Dithered: • No artifacts Dithered distribution • Difficult to reproduce Seite 21 © Fraunhofer ILT Abberation plots Raytracing software offer a number of diagrams and plots for analysing the aberrations of an optical system: • Wave front aberrations (Optical Path Difference: OPD) TRF • Transverse ray aberration (Transverse Ray Fan: TRF) • Spot diagrams • Encircled energy plots • Modulation transfer function (MTF) • Point Spread Function (PSF) encircled energy OPD Spot Seite 22 © Fraunhofer ILT Calculation of the encircled energy PEP 2R To every ray with index i in the entrance pupil a portion of the overall energy Etot is assigned: ri RTot ETot eri 1 ei = e(ri) ri 0 2R Ges The energy EEP(R) encircled in the radius R is calculated by radially summarizing: Spot diagram in the image plane R EEP R e ri ri 0 Seite 23 © Fraunhofer ILT Example: encircled energy • Focussing of a parallel ray bundle (with aberrations) Image plane V:\A991\2004\VORTRAG\VORLESUNG_TOS_I\05_RayTracing\Links\ • Summation of ZemaxBeispiele\EncircledEnergy.zmx the energy increments in the image plane Geometrical optics Diffraction limit Ray tracing with aberrations V:\A991\2004\VORTRAG\VORLESUNG_TOS_I\V01\06_RayTracing\ Animationen\ZemaxBeispiele\EncircledEnergy.zmx Anteil der eingeschlossenen Leistung Anteil der eingeschlossenen Seite 24 © Fraunhofer ILT Abberation plots Raytracing software offer a number of diagrams and plots for analysing the aberrations of an optical system: • Wave front aberrations (Optical Path Difference: OPD) TRF • Transverse ray aberration (Transverse Ray Fan: TRF) • Spot diagrams • Encircled energy plots • Modulation transfer function (MTF) • Point Spread Function (PSF) encircled energy OPD Spot Seite 25 © Fraunhofer ILT Modulation transfer function (MTF): definition Example: Object pattern Image pattern d I I Mod Max Min IMax IMin I Max IMax I(x) I(x) I IMin Min 0 0 x x Mod 1 Mod 0,7 Mod MTF( ) Bild 0,7 For a spatial frequency ModObj =1/d in „lines/mm“ Seite 26 © Fraunhofer ILT Modulation transfer funktion (MTF): Example Partly corrected focusing triplet with two field angles: 0° (blue) and 3°(green) No aberrations, no diffraction: Only diffraction, MTF1() MTF() = 1 MTF No aberrations, only Aberrations and diffraction diffraction: for two field angles, MTF1,2() MTF1() Aberrations and Spatial frequency (Lines/mm) diffraction: SeiteMTF 27 1(), MTF2() © Fraunhofer ILT Aberration plots Raytracing software offer a number of diagrams and plots for analysing the aberrations of an optical system: • Wave front aberrations (Optical Path
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